cognitive-discovery-platform 0.5.0

Pure Python computational science toolkit — quantum simulation, FFT, optimization, probability, statistics, and more.

Cognitive Discovery System (CDS)

Open-source computational science toolkit for research, simulation, and discovery.

CDS brings together quantum computing simulation, statistical analysis, signal processing, optimization, probability, and scientific computing in a single, dependency-light Python package. Every module is pure Python — no NumPy or SciPy required.

The project also includes built-in support for structured hypothesis generation, making it easier to explore ideas and connect them to simulation or analysis tools.

Currently in alpha (v0.5.0). Contributions welcome!

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🚀 Latest Update: Achieved 95%+ Test Coverage with 350 tests! Refactored the core with O(N³) pure-Python Partial Pivoting LU decomposition, vectorized machine learning optimizers, and parallelized Multi-Core Monte Carlo engines—all while maintaining strict zero-dependency architecture and resolving numerical instability risks.

Why CDS?

• Zero heavy dependencies — pure Python implementations you can read and learn from
• Quantum simulation — single & multi-qubit circuits with entanglement
• Built for discovery — hypothesis generation with structured outputs (assumptions, predictions, confidence) plus a Protocol for custom implementations
• Broad scope — 14 modules covering math, physics, stats, ML, signals, optimization, graph theory, ODEs, Monte Carlo
• 350+ tests (see CI) — thoroughly tested with 95%+ code coverage
• Practical automation — workflows for PR checklists, dependency updates, and releases to keep maintenance manageable
• CLI included — interactive tools, demos, and ASCII visualization from your terminal

Citing CDS

If CDS is useful in your research or publications, please cite it using the information in CITATION.cff at the repository root. This helps give proper credit and track adoption in scientific work.

Modules

Module	Description
cds.quantum	Single & multi-qubit simulation — Hadamard, Pauli, CNOT, SWAP, Toffoli, Bell/GHZ states, entanglement detection
cds.optimization	Gradient descent, Newton's method, Adam optimizer, golden section search
cds.ml	NEW: Pure Python Neural Networks — MLP, dense layers, Adam-based training
cds.signals	DFT, radix-2 FFT/IFFT (O(N log N)), 2D FFT/IFFT, convolution, power spectrum, filtering
cds.probability	Gaussian, uniform, exponential, binomial, Poisson distributions
cds.stats	Descriptive stats, Pearson correlation, linear regression, t-test, chi-square, ANOVA
cds.math_utils	Numerical calculus, O(N³) LU / QR / Cholesky, eigenvalue (power iteration), Gram-Schmidt, matrix inverse
cds.data_analysis	NEW: Mini-Pandas DataSet for filtering/grouping, CSV loading, ASCII visualization
cds.scientific	Physical constants, formulas (KE, gravity, gas law, Schwarzschild, de Broglie, escape velocity)
cds.graph	BFS, DFS, Dijkstra shortest path, Kruskal MST, topological sort, cycle detection
cds.montecarlo	Monte Carlo integration, π estimation, Buffon's needle, random walks (1D/2D)
cds.diffeq	Euler method, RK4, midpoint method, ODE system solver
cds.hypothesis	Structured hypothesis generation with prompt templates for custom research workflows

Quick Start

git clone https://github.com/Furox88/cognitive-discovery-system.git
cd cognitive-discovery-system
python -m venv .venv
source .venv/bin/activate
pip install -e ".[dev]"

# Run tests
pytest

# CLI usage
cds --help
cds constants
cds calc ke
cds modules
cds hypothesis "What causes the Hubble tension?"

🌐 Interactive Dashboard

CDS now features an Interactive Web Dashboard for real-time scientific exploration. Launch it directly from your terminal:

pip install "cognitive-discovery-toolkit[dashboard]"
cds dashboard

The dashboard includes a live Hypothesis Engine, Quantum Circuit Simulator, Neural Network training visualizer, and Statistical testing lab.

🧪 Scientific Case Studies

Explore how CDS is used to solve real-world research problems:

1. Hubble Tension Analysis: Generating and testing hypotheses for the expansion rate of the universe.
2. Quantum-ML Integration: Using quantum circuit measurements as features for classical Neural Network training.

Examples

See the examples/ directory for runnable demos and docs/research-workflows.md for guidance on embedding CDS in research pipelines.

Hypothesis Generation (cognitive discovery)

# Basic demo
python examples/hypothesis_demo.py

# With stats / experiment sketch example
python examples/hypothesis_with_stats_demo.py

# Custom generator implementation (using the HypothesisGenerator Protocol)
python examples/hypothesis_custom_generator.py

# Or via CLI
cds hypothesis "What causes the Hubble tension?"

Quantum Circuit (single qubit)

from cds.quantum import QuantumCircuit, hadamard, pauli_x, simulate

circuit = QuantumCircuit().add(hadamard()).add(pauli_x())
result = circuit.run()
print(result.probabilities())

counts = simulate(circuit, shots=1000)
print(counts)  # {0: ~500, 1: ~500}

Multi-Qubit & Entanglement

from cds.quantum import (
    QuantumRegister, h_gate, cnot, bell_state,
    ghz_state, is_entangled,
)

# Bell state (|00⟩ + |11⟩) / √2
reg = bell_state(0)
print(is_entangled(reg))  # True
print(reg.measure_shots(shots=1000))  # {'00': ~500, '11': ~500}

# 4-qubit GHZ state
ghz = ghz_state(4)
counts = ghz.measure_shots(shots=1000)
print(counts)  # {'0000': ~500, '1111': ~500}

Optimization

from cds.optimization import gradient_descent, newton_method

# Find minimum of (x-3)²
result = gradient_descent(lambda x: (x - 3) ** 2, x0=10.0, lr=0.1)
print(f"x = {result.x:.6f}")  # ~3.0

# Find √2 using Newton's method
result = newton_method(lambda x: x ** 2 - 2, x0=1.5)
print(f"√2 = {result.x:.10f}")  # 1.4142135624

Signal Processing

from cds.signals import dft, fft_radix2, convolve, low_pass_filter

# FFT of a signal
signal = [complex(i) for i in range(8)]
spectrum = fft_radix2(signal)

# Convolution
result = convolve([1.0, 2.0, 3.0], [0.5, 0.5])
print(result)  # [0.5, 1.5, 2.5, 1.5]

Probability Distributions

from cds.probability import gaussian_pdf, binomial_pmf, poisson_pmf

# Gaussian PDF at x=0
print(gaussian_pdf(0.0, mu=0, sigma=1))  # 0.3989...

# Binomial: P(3 heads in 5 fair flips)
print(binomial_pmf(3, 5, 0.5))  # 0.3125

# Poisson: P(k=2, λ=3)
print(poisson_pmf(2, 3.0))  # 0.2240...

Statistics

from cds.stats import mean, stdev, correlation, linear_regression

data = [12.5, 14.3, 11.8, 15.1, 13.7]
print(f"mean={mean(data):.2f}, std={stdev(data):.2f}")

x = [1, 2, 3, 4, 5]
y = [2.1, 3.9, 6.2, 7.8, 10.1]
reg = linear_regression(x, y)
print(f"y = {reg.slope:.2f}x + {reg.intercept:.2f}, R²={reg.r_squared:.3f}")

Scientific Computing

from cds.scientific import kinetic_energy, escape_velocity, get_constant

print(get_constant("c"))          # speed of light
print(kinetic_energy(10, 5))      # 125.0 J
print(escape_velocity(5.972e24, 6.371e6))  # ~11186 m/s

Graph Theory

from cds.graph import Graph, dijkstra, kruskal_mst, bfs

g = Graph(n_vertices=4, directed=False)
g.add_edge(0, 1, 1.0)
g.add_edge(1, 2, 2.0)
g.add_edge(2, 3, 3.0)
g.add_edge(0, 3, 10.0)

dist, prev = dijkstra(g, 0)
print(dist)  # {0: 0.0, 1: 1.0, 2: 3.0, 3: 6.0}

edges, total = kruskal_mst(g)
print(f"MST weight: {total}")  # 6.0

Monte Carlo Simulation

import math
from cds.montecarlo import estimate_pi, mc_integrate

if __name__ == "__main__":
    # Unit-circle method
    result = estimate_pi(n_samples=100_000, seed=42)
    print(f"PI approximation: {result.estimate:.4f}")

    # Integration
    area = mc_integrate(math.sin, 0, math.pi, n_samples=100_000)
    print(f"Integral of sin(x): {area.estimate:.4f}")

Differential Equations

from cds.diffeq import rk4, solve_system
import math

# dy/dt = -y, y(0)=1  =>  y(t) = e^(-t)
sol = rk4(lambda t, y: -y, t0=0, y0=1.0, t_end=2.0)
print(f"y(2) = {sol.y[-1]:.6f}")  # ~0.135335 (e^-2)

# Harmonic oscillator: x'' = -x
def harmonic(t, y):
    return [y[1], -y[0]]
t_vals, y_vals = solve_system(harmonic, 0, [1.0, 0.0], math.pi)
print(f"x(π) = {y_vals[-1][0]:.4f}")  # ~-1.0

Architecture

src/cds/
├── quantum/        # Quantum circuit simulation (single & multi-qubit)
├── optimization/   # Gradient descent, Newton, Adam, line search
├── signals/        # DFT, FFT, convolution, filtering
├── probability/    # Probability distributions & sampling
├── stats/          # Statistical analysis & regression
├── math_utils/     # Calculus, linear algebra, eigenvalues, Gram-Schmidt
├── data_analysis/  # CSV loading & data transforms
├── scientific/     # Physical constants & formulas
├── graph/          # Graph algorithms (Dijkstra, BFS, DFS, Kruskal MST)
├── montecarlo/     # Monte Carlo methods (π, integration, random walks)
├── diffeq/         # ODE solvers (Euler, RK4, midpoint)
├── hypothesis/     # Hypothesis generation
├── core/           # Shared models, config
└── cli.py          # Command-line interface

examples/           # Runnable demo scripts
tests/              # 350 tests (see CI)
docs/               # Documentation (getting started, API reference, benchmarks)

.github/workflows/  # Automation for PRs (labels + checklist), releases, and dependency updates

Vision

The long-term goal of CDS is to provide a lightweight, dependency-free toolkit for scientific exploration and discovery.

We aim to combine solid numerical foundations (quantum simulation, FFT, linear algebra, statistics, differential equations, etc.) with higher-level tools for hypothesis generation and research workflows.

A distinctive part is the cds.hypothesis module, which generates structured, falsifiable hypotheses with explicit assumptions and predictions. The cds hypothesis CLI command and examples/hypothesis_demo.py make this side immediately usable. Recent work has focused on making the CLI and docs more practical for day-to-day use while keeping everything readable pure Python.

The project is still early but is being actively developed with a focus on code quality, test coverage, documentation, and usability for researchers and students.

Run cds modules after installation to explore the current modules.

Recent improvements

Recent updates have aimed to make it simpler to generate and explore ideas within the toolkit:

• New CLI commands for browsing available modules and experimenting with hypothesis generation
• A dedicated example showing how to use the hypothesis features end-to-end
• Automation around pull requests, dependency management, and releases to free up time for core scientific work

The goal is to lower the barrier for using the discovery-oriented parts of the project and reduce time spent on routine tasks.

Contributing

See CONTRIBUTING.md for setup and guidelines.

Looking for:

• Researchers with domain expertise
• People interested in pure-Python scientific computing
• Contributors for new modules (ML basics, PDE solvers, etc.)
• People who want to help make scientific tools easier to maintain and use

Automation and Maintenance Workflows

A few GitHub Actions handle repetitive aspects of keeping the project running:

• Dependabot for regular updates to dependencies and GitHub Actions
• Automatic labeling and review checklists for pull requests
• A release process that builds and publishes on version tags

These help ensure that time spent on the project goes more toward developing new modules, improving hypothesis tools, and supporting research use cases rather than manual upkeep.

See .github/workflows/ for the current setup.

License

MIT — see LICENSE.

Contact

• Maintainer: @Furox88
• Issues & Discussions: GitHub

Why These Automations Exist

The project is maintained by a small team (often solo). The workflows above exist so that routine tasks (labeling PRs, running checks, cutting releases, keeping dependencies fresh) take as little time as possible. This frees hours for actual research work: improving the hypothesis tools, adding new scientific modules, writing better examples, and exploring new discovery workflows.

If you're a researcher or educator using CDS, these automations mean you can focus on the science instead of repo housekeeping.